Method of measuring the thickness of thin coatings



Oct. 14, 1947. H. FRBEDMAN 2,428,796

METHOD OF MEASURING THE THICKNESS OF THIN COATINGS Filed Sept. 8, 1944 2Sheets-Sheet l AXIS OF SPECTROMETER gvvumvT O'L HERBERT FRBEDMAN ()ct14, 1947. H. FRIEDMAN 2,428,796

METHOD OF MEASURING THE THICKNESS OF THIN COATINGS Filed Sept. 8, 1944 2Sheets-Sheet 2 COPPER FILM THICKNESS VS. lNTENSlTY RATIO 10- lolO' THICKN ESS .IN CENTE M ETERS I ELELQ ALUMINUM FILM THICKNESS VS. INTENSITYRATIO IO' 10" :0' no THICKNESS IN CENTIMETERS 3 H ERBERT FRIEDMANvarious items.

Patented Oct. 14, 1947 METHOD -GE'MEASUBING THE TRIGKNESS THIN;COATINGS.

Herbert Friedman ArlingtomVa. Y

Application September 8,, 1944, Seth! No. 553,262

14 Claims. (01. 250-83) (Granted under the act of March 3, 18-83, asamended April 30, 1928; 370 O. G. 757) My invention relates to themeasurement of small dimensions andparticularly to the nondestructivemeasurement of the thickness of 4 thin coatings deposited on crystallinebacking materials. v I

In the past many methods have been devised for the estimation of thethicknesses of thin coatings deposited on materials, for example, thethickness of a plated metal coating on a base metal. These methods offilm thickness measurement involve, generally, chemicalstripping of thefilm from the surface by means of standard chemical solutions,micrometric measurements and magnetic measurements. However, most ofthese methods involve the destruction of the sample tested and merelygive an indirect measure or estimate of the thickness of a similarcoating deposited ona similar material under conditions comparable tothose under which the coating was deposited on the sample tested.

It has long been recognized in the electroplating art that anon-destructive rapid method of measuring plating thicknesses would beof great, 7,

value. More. recently considerable interegf'has been shown by the paintindustry in the study of the thickness of paint films and consequentlyin the nature of the surfaces of pigment particles. Also, recently, themanufacture of ultra-high frequency radio parts and equipment hasintensified the need for a rapid, non-destructive method'for measuringthicknesses of films in the form of sputtered gold andsilver and othercoatings on It is the principal object of my invention to provide anon-destructive method of measuring the thickness of thin coatings,metallic or nonmetallic, on crystalline backings to a degree pfprecision hitherto unattainable.

A secondary object of my invention is to make 7 possible such filmthickness measurement-s from one side of the coated surface.

Another object of my invention is to provide for the measurement of theindividual thicknesses of several different superimposed coatings on agiven backing material.

A further object o! my invention is to provide for the measurement ofcoating thickneses over areas as large as one square inch or as small asone square millimeter.

A still further object of my invention is to provide for the measurementof the thickness of 'a coating on a surface of any shape whatever.

Another additionalobject of my invention re- 7 si es in the provision ofa method of measuring-- the thicknessotacoating on finely dividedmaterials such as pigments or other finely divided powders.

A further additional object of my invention is to provide for theprecise measurement of the thicknesses of thin metal foils.

Further objects and advantages of my invention will in part be obviousand in part appear hereinafter.

My invention comprises the method of measuring film thicknesses bymeasuring the X-ray diffraction pattern intensity of a material on whichthe film,is-applied and comparing its intensity with that of thebacking. material alone and thus obtaining an extremely precise estimateof the thickness of the film. The method of Dre- Ew my invention will bedescribed in defiafi i t following p a s taken in qniunction with theaccompanying drawings, of. whi

Figure 1 is a diagrammatic sketch, of the arrangement of an X-raysource, specimen and detector illustrating the inter relationship ofparts of apparatus used in taking X-ray diffraction patterns;

Figure 2 is a diagrammatic representation of a novel method of placing acoated specimen in an X-ray spectrometer according to my invention;

Figures 3 and 4 are sample calibration curves by means of whichintensity ratios of diffraction the principle of patterns can beconverted into film thicknesses with X-rays of various wavelengths. Thecurves apply to copper and aluminum films respectively.

Thickness measurements made by determination of X-ray transmissionthrough materials are based on the exponential absorption law in whichIx is the transmitted intensity, In the initial intensity, ,4 the massabsorption coefficient, p the density of the material irradiated and a:the thickness of the irradiated material. For most materials the massabsorption coefficient and .the density p are known or are readilymeasured. The ratio of transmitted to incident intensity,

Ix/IO, may be measured photographically, by

one side of a specimen, the beamof radiation must be reflected from thebacking material. All crystagn e materials reflect monochromatic X! i frbe drawn through the series of three poi one rays coherently atspecific angles given by the Bragg diffraction formula,

in which 7t is the X-ray wavelength, (1 the crys-' talline spacinggiving rise to a reflection at the angle a and n is the order of thediffraction. Every crystalline material has a unique set of planarspacings, (ink) and associated reflection angles 011111.

My method of measuring the thickness of a coating deposited on acrystalline backing can be more clearly understood by a consideration ofthe above theoretical basis therefor in conjunction with the drawings.Referring to Figure 1. in which the conventional apparatus arrangementfor taking an X-ray diifration pattern is illustrated, i is acrystalline backing material, II a coating on it, l2 an X-ray source, l3an X-ray detector. By means of collimators l4 and IS the specimen isexposed to a beam of parallel X-rays, and a beam of parallel rays isdetected. If 10 is the intensity of the radiation reflected from theuncoated backing material, the ratio Ix/IO' is given as follows:

ing material, Xe is the thickness of the coating, and 0 is thecharacteristic angle of reflection of the X-rays from the backingmaterial. If the ratio of Ix/IO is determined, Xe can be readilycomputed. In determiningthe value of Ix/Io and, thus,

a coating thickness, it is desirable first to measure Io for theuncoated specimen, cbatia eplace it in the diffraction apparatus, andm'easure Ix.

If it is impossible to measure It on the uncoat d specimen, acorresponding measurement made on an -uncgated specimen of the samecomposition will give aTatiITw measurement of the coating thic e InFigure 2, I have illustrated a method of mounting a specimen in aspectrometer in a man- 45 and immediately underlyin ner such thatdiffraction patterns of much improved intensity can be obtainedtherefrom. This is based upon the theorem of plane geometry that allangles inscribed in a chord of a circleare equal. In the figure, 20represents the source of the X-rays, 2| a slit, 22 the specimen beinexamined, 23 a second slit and 24 a detector. The three points 2|, thespectrometer axis, and 24 constitute three points through which a circlecan be drawn. Of these points, 2| and 22 remain fixed and 24 varies inposition as the diffraction pattern of the specimen is scanned.Nevertheless, no matter what position 24 takes, a circle can be drawnthrough all three points. It is apparent that if a scanning of adiffraction pattern by varying the position of 24 through a 90 are beaccomplished a large number of circles can fofeachposition of 24.; Itshould be noted that n the specimen is mounted at the axis of thespectrometerang is exposed to a divergent beam of X-rays. ThedetTtoriHamovedjn an arc of a circle about the axis of the spectrometerto detect the lines of the X-ray diffraction pattern. ;If the radius ofthe circle defined by the points 2|, the spectrometer axis and 24 islarge compared to the width of thespecimen the specimen, withoutappreciable error, can be saictto conform to an arc of the circle andall radiation striking it 7 measured ratio Ix/Io is then expressed by.

in which the detector moves. In this manner, the detector is exposed toan intensifiedzdifiraction pattern of the specimen.

In Figures 3 and 4 there are shown calibration curves for estimating thethicknesses of copper coating and the ratio of the transmitted to theincident radiation. The curves are plotted with the ratio of transmittedto incident intensity as a function of coating thickness using the X-raytube targets and angles noted on the curves.

Similar curvescan be prepared for films or any material deposited on anycrystalline backing ma- I terial. It is evident that by selection of anappropriate X-ray tube target and angle, film thickness measurements canbe made using the mid portions of the curves where the slopes are bestadapted to precise readings.

When it is desired .to measure the individual thicknesses of severalcoatings deposited on a crystalline backing, as, for example, theindividual 25 thicknesses of the copper, nickel, and chromium layers ona so-called chromium plated article, the following technique can beemployed: The ratio of transmitted to incident intensity is measin whiche is the mass absorption coefllcie1it of\ d and the equations:

theegating material, pc is the density of the coatand are solved for thethickness of the top layer. In

the equations the symbols are defined as follows: The symbols have themeanings given above,

40 but the subscripts refer to the top and underlying respectively. Thesymbols N1 and N:

' in turn give a reliable repreSntWic weights of the elements referredto by the s A second solution to ain the sum of the top termined. If thebacking surface is rough but not so rough as to permit undercutting bythe coating,

the mass of the coating per unit area is obtained by the'solving for r?V .7

When it is desired to measure the thickness of non-metallic coatings, atwo-element compound is treated as two superimposed monatomicstructures. signed individually to the several elements forming thecompound. For example, if a compound having a general formula AB andhaving a density. P, in which the atomic weights of the elementscomprising the compound are NA and NB the following relationships willhold:

as aegi a PB a and PA PB P from which n and p13 can be computed. 'Thewill be focused at a point. on the arc of the circle in which x is thethickness of the compound layer is made, the.

Density absorped coefllcientscan beas-" niques' with a measurement ofthei particle diameter of the powder will yield reliable results.

This technique for measuring films, as can be seen, is applicable tomeasurement of the thickness of electroplated deposits, oxide films onmetal surfaces, oxide films 'on, finely divided metals or materials,sputtered metal coatings on materials such as are commonly found inmodern ultra high frequency electrical parts and metal foils. Thethicknesses of foils are commonly measured by transmission methods, but,by laying the foil on a crystalline backing and taking a diflractionpattern as pointed out above, the precision of the measurement is muchimproved for a double absorption occurs in the foil and no difllculty isexperienced in orienting the foil with respectto the- X-ray beam. v

It is not necessary that the specimen be plane in order to measurecoating thickness. By reducing the area of the specimen exposed to thebeam, the specimen, regardless of curvature can be made to approximatethe arc of the circle defined in Figure 2. I have found that precisemeasurements of coating thickness can be made on areas as small as onesquare millimeter.

The diffraction pattern can be taken by means of standard X-raydiffraction apparatus and the intensity of-the pattern can be measuredwith standard photographic apparatus. However, a great deal of time canbe saved by using a Geiger Muller tube as the detector of the pattern.When using a Geiger Muller tube as a detector, any degree of precisionin the intensity measurement can be attained by extending the time ofmeasurement, i. e., the number of counts. Using the Geiger Mullerdetector the time consumed in making the necessary measurements iscounted in minutes for a single strong line of the diffraction patterncan be selected for the intensity measurements.

' It is incorrect to assume that Ix in the equations I is made upentirely of K: radiation transmitted through the layer. If any materialis irradiated with X-rays harder than the minimum required to ionize theK shell,the entire fluorescent X-ray spectrum is excited. Even if the Kmradiation of the target employed is softer than the radiation requiredto excite fluorescence, there are always present in the continuousspectrum X-rays of much shorter wavelength than the Kw lines.,Fluorescent rays excited by the high energy end of the continuousspectrum and general scattering contribute an appreciable backgroundradiation. The influence of background radiation on measurement ofthickness by the method described above may be considerably reduced bythe use of suitable filters or almost completely removed by means of acrystal monochromator. but this latter step is generally unnecessary.The cohercut reflection from reasonably well formed crystallinematerials is limited to. an angular range a less than one degree in 20.A measurement of intensity of the background radiation away from thisline, gives the extra intensity due to general and fluorescentscattering. Subtracting this background from the total intensitymeasured at the Bragg angle leaves only the intensity truly transmittedthrough the thin layer,

The advantages of my method of measuring fllm thicknesses can besummarized as follows: Standard X-ray diffraction apparatus can be used;

Specimens of any shape can be used; Measurement can be made on finelydivided materials; I The,coatingthickness measurement is nondestructive;

Individual thicknesses of superimposed coatings can be measured;

Thicknesses of metallic and non-metallic coatings can be measuredequally well;

Theradiation intensity measurement is'helpe by a double absorption ofradiation occurring in the coating, once before and once afterreflection from the backing material;

By using a specimen of relatively large area and a divergent beam ofX-rays, a diffraction pattern of improved intensity can be obtained.with resultant improved precision in the measurement.

From the foregoing, the method of practicing my invention will be fullyunderstood, but it is to be understood that the invention is notrestricted to the present disclosure to any extent otherwise thanrestricted by the manner in which such invention is'claimed.

The invention described herein may be manufactured and used by or forthe Government of the United States of America for governmental purposeswithout the payment, of any royalties thereon or therefor.

Having described my invention, what ,Iclaim as new and wish to secure byLetters Patent is:

' l. The method of measuring the thickness of a coating on a crystallinematerial comprising directing a beam of X-rays onto said coatedmaterial, intercepting rays comprising lines of the diflraction patternof the crystalline material and determining their intensity as comparedwith the intensity of similar lines from the uncoated crystallinematerial. I

' 2. The method of measuring the thickness of a coating on a crystallinematerial comprising directing a beam of X-rays of known intensity ontosaid material, intercepting rays comprising lines of the diffractionpattern of the crystalline material and determining their intensity ascompared with the intensity of. similar lines obtained from the uncoatedmaterial.

3. The method of measuring the thickness of a coating on a crystallinematerial comprising directing a beam of X-rays onto said material,intercepting and determining the intensity of lines of the diffractionpattern of the said crystalline material, comparing said line intensitywith the intensity of corresponding lines from the uncoated material,and thus obtaining a measure of the coating thickness.

i. The method of measuring the thickness of a coating on a surface ofcrystalline material from oneside thereof which comprises directing abeam of X-rays onto said surface and determining from the same side ofsaid surface the intensity of lines of the diffraction pattern of thesaid crystalline material as compared with the intensity of like linesobtained from the uncoated material.

5. The method of measuring the thickness of a coating on a crystallinematerial comprising directing a beam of X-rays onto said coated surface,at an acute angle thereto, intercepting rays comprising lines of thediffraction pattern of the crystalline material and comparing theirintensity with the intensity of corresponding lines obtained fromtheuncoated material, thereby obtaining a measure of the coatingthickness.

6. The method of measuring the thickness of a metallic coating on asurface of crystalline material from one side thereof, which comprisesdirecting a divergent beam of X-rays onto said surface and determiningfrom the same side thereof the intensity of lines of the diffractionpattern of the said crystalline material as compared with the intensityof like lines obtained from the uncoated material.

7. The method of measuring the thickness of foil comprising backing saidfoil with a crystalline material, directing a beam of X-rays onto saidbacked foil, intercepting and determining the intensity of lines of thediffraction pattern of the backing material, comparing the intensitythereof with similar lines from the backing material alone and thusobtaining a measure of'the thickness of the foil.

8. The method of measuring the thickness of an electrodeposited metalliccoating on a crystalline material from one side thereof comprisingdirecting a .beam of X-rays onto said surface and determining from thesame side thereof the intensity of lines of the diffraction pattern ofthe said crystalline material as compared with the intensity of likelines obtained from the uncoated material.

9. The method of measuring the thickness of a coating on a crystallinematerial comprising directing a beam of X-rays onto. said coatedmaterial, intercepting rays comprising a line of the diffraction patternof the crystalline material, determining the intensity of the line, andcomparing its intensity with the intensity of a corresponding line fromthe uncoated crystalline material.

10. The methodof measuring the thickness of a coating on a crystallinematerial comprising directing a beam of X-rays onto said coatedmaterial, intercepting'and determining the intensity of a line of thediffraction pattern of the said crystalline material, comparing thatline. in-

tensity with the intensity of a corresponding line" from the uncoatedcrystalline material, and thus obtaining a measure of the coatingthickness.

.11. The method of measuring the thickness of a metallic coating on thesurface of crystalline 'backed foil, interceptingand determining. the

intensity of a line of the diffraction pattern of the backing material,comparing the intensity thereof with the intensity of a correspondingline from the backing material alone, and thus obtaining a measure ofthe thickness of the foil.

13. The method of measuring the thickness of an electrodepositedmetallic coating on a crystalline material from oneflsidethereofcomprising directing a beam of X-rays onto the coated surface anddetermining from the same side thereof the intensity of a line of thediffraction'pattem of the said crystalline material, comparing theintensity of the said line with the intensity of a corresponding .linefrom the uncoated material, and obtaining thereby a measure of thethickness of the deposit.

14. The method of measuring the thickness of a coating on acrystallinematerial comprising directing a beam of X-rays onto said coated surface,intercepting rays comprising alline of the diffraction pattern of thecrystalline material and measuring the intensity thereof, comparing theintensity of said line with the intensity, of.

a corresponding line obtained from the uncoated material, and therebyobtaining a measure of the coating thickness.

HERBERT FRIEDMAN.

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATEN'I'S Brucei. May 11, 1943

